Question: Simplify the following expression: $k = \dfrac{r^2 + 10r + 9}{r + 1} $
Explanation: First factor the polynomial in the numerator. $ r^2 + 10r + 9 = (r + 1)(r + 9) $ So we can rewrite the expression as: $k = \dfrac{(r + 1)(r + 9)}{r + 1} $ We can divide the numerator and denominator by $(r + 1)$ on condition that $r \neq -1$ Therefore $k = r + 9; r \neq -1$